


















Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Community
Ask the community for help and clear up your study doubts
Discover the best universities in your country according to Docsity users
Free resources
Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors
This solution manual provides solutions to the problems in the 6th edition of applied multivariate statistical analysis. It was prepared with the help of various computer software and includes solutions to exercises in each chapter. The manual is intended as an aid for instructors and adopters of the textbook.
Typology: Assignments
1 / 26
This page cannot be seen from the preview
Don't miss anything!
This solution manual was prepared as an aid for instrctors who wil benefit by
parcularly in those problems involving long chains of arthmetic calculations.
51i = 4.
.ì
Chapter 1
522 = 3.56 S12 = 3.
...^.
.. .
12~
..
7..^. .. 5. (^)..
0 2 4 6 8 10 12 xl
b) SlZ is negative
Xi =5.20 x2 = 12.48 sii = 3.09 S22 = 5. SI2 = -15.94 'i2 = -.
x = 12. ( 3.
R =( 1 -.98)
1.5 a) There is negative correlation between X2 and X3 and negative correlation
Sêåttêr'Plotäl'(i'Marginal.DotPiØ_:i..~sxli.
1600
M)C (^). (^). (^)..^.
400
. (^)...^.^.^.^. 0
. '-' . .Scatiêr;Plötànd:Marginal.alÎ.'llÎi:lîtfjtì.I... ......^.^.^.^. 1600 ..
400
....^.^.^. 0 50 100 150 200 250 300 xl
1.5 b)
x = 14.
R = ( ~ -.
HIDDLE OF INTERVAL
HIDDLE OF INTERVAL
HIDIILE OF INTERVAL
J.
HIDDLE OF INTERVAL
-.85)
1
. 1
Xs
HIDIILE OF NUMB£R. OF NUMBER OF INTERVAL 08SERVATIONS OBSERVATioNS cooJ.^2 **
5 un*^ 10. 4 ****
1 * (^) LS. 1 * J n* (^) 19. 0
2 n 1 * (^) I' I DOLE .OF INTE"RVAL
X
NUHBER OF OBSERVA T I'ONS 1 *
19 ******************* 9 ********* .3 U* S u***
X
NUMBER OF. OBSERVA T IONS 1 J *$********* 15 *************** a ******** 5 ui 1 *
HIDDLE OF INTERVAL
J.
s.
NUMBER OF OBSERVATIONS 7 ******* 25 ************************* 9 ********* 1 *
NUltEiER OF OI4SERVATIOllS J *** 4 ****
7 ******* B ******** 5 n*** 2 ** 2 u 1 * o o 2 ** 1 *
X
1.8 Using (1-12) d(P,Q) = 1(-1-1 )2+(_1_0)2; = /5 = 2.
Using (1-20) d(P.Q)' /~H-1 )'+2(l)(-1-1 )(-1-0) '2t(-~0);' =j~~ = 1.38S
Using (1-20) the locus of points a c~nstant squared distance 1 from Q = (1,0)
is given by the expression t(xi-n2+ ~ (x1-1 )x2 + 2t x~ = 1. To sketch the
locus of points defined by this equation, we first obtain the coordinates of
some points sati sfyi ng the equation:
(-1,1.5), (0,-1.5), (0,3), (1,-2.6), (1,2.6), (2,-3), (2,1.5), (3,-1.5)
The resulting ellipse is:
X
X
. .
..
. . . -"
Therefore this is a distance for correlated variables if it is non-negative
for all values of xl' xz' But this follows^ easily if we write
b) In order for this expression to be a distance it has to be non-negative for
conclude that this is not a validdistan~e function.
d(P,Q) = 14(X,-Yi)4 + Z(-l )(x1-Yl )(x2-YZ) + (x2-Y2):¿'
= 14(Y1-xi):¿ + 2(-i)(yi-x,)(yZ-x2) + (xz-Yz):¿' = d(Q,P)
Next, 4(x,-yi)2. - 2(xi-y,)(x2-y2) + (x2-YZ): =
The s€cond term is zero in this last ex.pr.essi'on only if xl = Y1 and
then the first is zero^ only if x.2 = YZ.
1.14 a)
360.+ )(
320.+
280.+
240.+
200.+
.
. .
.. . .
. ....
.. .. . .. I: I:
. ... .. .
160.+ (^) +______+_____+-------------+------~.. )(
Strong positive correlation. No obvious "unusual" observations.
b) Mul tipl e-scl eros; s group.
116.91 61 .78^ -20.10^ 61. 1 3^ -27. 65
(synetric) 337.
.61 .11^ .12^ .39^ -.
;. (synetric).
1 -. 01 0
(syretric) 1
The largest correlation is between appetite and amount of food eaten.
Both activity and appetite have moderate positive correlations with
symptoms. A1 so, appetite and activity have a moderate positive
correl a tion.
RADIUS o _R A 0 IUS
I
c- c.. c,.
o' '
.. o' (^) : .' '. " "^ .' .. CI - .... (^) .QI- (^) ..-
C - C...^ C,.
.,.
.'
. :; ..
". 00 o. :^ 00. .. : ..
.~.,.. .. ..^ -
II - (^) ..I:^ I:,.
,
0'
, i:: ,^ 0,^. 'o'
II - (^) ..I: (^) ~C
" (^) .0 ,. .- " o'^. .. ,. (^) " 00
I: - C.. C,.
: "
. .. : .. (^) " ,,'
co co^ CI UI.. ..-^ - ..
I: - C.. C,. .. co^ ..
'. ".
. 0,
". .
.. QI ..'" CD-
oi
;:o
en
oi
c: ¡c ..::
¡c ..
en
~. .... ". ... A. .c (^) ~l .,¡^ ..^ 'l
t.., .,.....^ .~. -Ii... P.~... _. .-,. .,. (^)..^. ..., ".
i: (^) l
.i (^) ~ ' tl,'^ !t 1" (^) .~.
to ... ....^ ...
l. t
.'
.
:. -i-. (^) ..(.. !,l :i^
.~ ~ -l
..'^ .0' :,... ....^.^. .1,. ..^. .- ,--.
~,:~
\
I! (^) ~ .': ~
.8., .,.. .. 'L. .~...
I.
.. ..,..^ t.:...^. ."^.^ "^.^. ......."
. (^) ~ ~;^
.~ (^) · .~c,.
. -it..^.^.^ ... lý~ ..... t-- ,. .-.. .t:....
.~,.
~..:
.~~. .~.
. ,. ..^ ll.. ..... ...^ ....... l.
. .
.~.
.1f
. .;;- ~:-\1: i: '.~: ~ ii^.. ~ :,.^ I.
l
" (^).... ... :. .. f
. ...
.
.
.
. .
..
.
.. . .. .
o
.^. .
X .
X .
.
Ó,e
~~ô 0'"
.
.
..
o
X
.
.
.
Outlier Q
. . .. .
. ...
.
G
X
. (^). . .. (^). ... ... ..^.^ .. fi.^. .. . (^) .. ..
.
~~ ~ø.
/ , X Xz/ ·
.
..
x,
. (^). . (^). .. ... .. (^)..^. .. .. . . (^).
.
Xz
.."
.. .. /
. ./ ./ ./ ./ ;I ./.
.
..
.
. .
. (^) ,. . ... fi .. .. (^). .. .. .
./
.. .~
..
x,
.
.. .. (^).
~~e
./ ~e~
..
..s..